M1 aberration (of light): the relativistic apparent angular displacement of the observed position of a celestial object from its geometric position, caused by the motion of the observer in the reference system in which the trajectories of the observed object and the observer are described. (See aberration, planetary.) aberration, annual: the component of stellar aberration resulting from the motion of the Earth about the Sun. (See aberration, stellar.) aberration, diurnal: the component of stellar aberration resulting from the observer s diurnal motion about the center of the Earth due to Earth s rotation. (See aberration, stellar.) aberration, E terms of: the terms of annual aberration which depend on the eccentricity and longitude of perihelion of the Earth. (See aberration, annual; perihelion.) aberration, elliptic: see aberration, E terms of. aberration, planetary: the apparent angular displacement of the observed position of a solar system body from its instantaneous geometric direction as would be seen by an observer at the geocenter. This displacement is produced by the combination of aberration of light and light time displacement. aberration, secular: the component of stellar aberration resulting from the essentially uniform and almost rectilinear motion of the entire solar system in space. Secular aberration is usually disregarded. (See aberration, stellar.) aberration, stellar: the apparent angular displacement of the observed position of a celestial body resulting from the motion of the observer. Stellar aberration is divided into diurnal, annual, and secular components. (See aberration, annual; aberration, diurnal; aberration, secular.) altitude: the angular distance of a celestial body above or below the horizon, measured along the great circle passing through the body and the zenith. Altitude is 90 minus the zenith distance. annual parallax: see parallax, heliocentric. anomaly: the angular separation of a body in its orbit from its pericenter. anomaly, eccentric: in undisturbed elliptic motion, the angle measured at the center of the orbit ellipse from pericenter to the point on the circumscribing auxiliary circle from which a perpendicular to the major axis would intersect the orbiting body. (See anomaly, mean; anomaly, true.) anomaly, mean: the product of the mean motion of an orbiting body and the interval of time since the body passed the pericenter. Thus, the mean anomaly is the angle from the pericenter of a hypothetical body moving with a constant angular speed that is equal to the mean motion. In realistic computations, with disturbances taken into account, the mean anomaly is equal to its initial value at an epoch plus an integral of the mean motion over the time elapsed since the epoch. (See anomaly, eccentric; anomaly, mean at epoch; anomaly, true.) anomaly, mean at epoch: the value of the mean anomaly at a specific epoch, i.e., at some fiducial moment of time. It is one of the six Keplerian elements that specify an orbit. (See Keplerian elements; orbital elements.) anomaly, true: the angle, measured at the focus nearest the pericenter of an elliptical orbit, between the pericenter and the radius vector from the focus to the orbiting body; one of the standard orbital elements. (See anomaly, eccentric; anomaly, mean; orbital elements.) aphelion: the point in an orbit that is the most distant from the Sun. apocenter: the point in an orbit that is farthest from the origin of the reference system. (See aphelion; apogee.)
M2 apogee: the point in an orbit that is the most distant from the Earth. Apogee is sometimes used with reference to the apparent orbit of the Sun around the Earth. apparent place (or position): the proper place of an object expressed with respect to the true (intermediate) equator and equinox of date. apparent solar time: see solar time, apparent. appulse: the least apparent distance between one celestial object and another, as viewed from a third body. For objects moving along the ecliptic and viewed from the Earth, the time of appulse is close to that of conjunction in ecliptic longitude. Aries, First point of: another name for the vernal equinox. aspect: the position of any of the planets or the Moon relative to the Sun, as seen from the Earth. astrometric ephemeris: an ephemeris of a solar system body in which the tabulated positions are astrometric places. Values in an astrometric ephemeris are essentially comparable to catalog mean places of stars after the star positions have been updated for proper motion and parallax. astrometric place (or position): direction of a solar system body formed by applying the correction for light time displacement to the geometric position. Such a position is directly comparable with the catalog positions of background stars in the same area of the sky, after the star positions have been updated for proper motion and parallax. There is no correction for aberration or deflection of light since it is assumed that these are almost identical for the solar system body and background stars. An astrometric place is expressed in the reference system of a star catalog; in The Astronomical Almanac, the reference system is the International Celestial Reference System (ICRS). astronomical coordinates: the longitude and latitude of the point on Earth relative to the geoid. These coordinates are influenced by local gravity anomalies. (See latitude, terrestrial; longitude, terrestrial; zenith.) astronomical refraction: see refraction, astronomical. astronomical unit (au): the radius of a circular orbit in which a body of negligible mass, and free of perturbations, would revolve around the Sun in 2π/k days, k being the Gaussian gravitational constant. This is slightly less than the semimajor axis of the Earth s orbit. astronomical zenith: see zenith, astronomical. atomic second: see second, Système International (SI). augmentation: the amount by which the apparent semidiameter of a celestial body, as observed from the surface of the Earth, is greater than the semidiameter that would be observed from the center of the Earth. autumnal equinox: see equinox, autumnal. azimuth: the angular distance measured eastward along the horizon from a specified reference point (usually north). Azimuth is measured to the point where the great circle determining the altitude of an object meets the horizon. barycenter: the center of mass of a system of bodies; e.g., the center of mass of the solar system or the Earth Moon system. barycentric: with reference to, or pertaining to, the barycenter (usually of the solar system). Barycentric Celestial Reference System (BCRS): a system of barycentric space time coordinates for the solar system within the framework of General Relativity. The metric tensor to be used in the system is specified by the IAU 2000 resolution B1.3. For all practical applications, unless otherwise stated, the BCRS is assumed to be oriented according to the ICRS axes. (See Barycentric Coordinate Time (TCB).) Barycentric Coordinate Time (TCB): the coordinate time of the Barycentric Celestial Reference System (BCRS), which advances by SI seconds within that system. TCB is related to
M3 Geocentric Coordinate Time (TCG) and Terrestrial Time (TT) by relativistic transformations that include a secular term. (See second, Système International (SI).) Barycentric Dynamical Time (TDB): A time scale defined by the IAU (originally in 1976; named in 1979; revised in 2006) for use as an independent argument of barycentric ephemerides and equations of motion. TDB is a linear function of Barycentric Coordinate Time (TCB) that on average tracks TT over long periods of time; differences between TDB and TT evaluated at the Earth s surface remain under 2 ms for several thousand years around the current epoch. TDB is functionally equivalent to T eph, the independent argument of the JPL planetary and lunar ephemerides DE405/LE405. (See second, Système International (SI).) Besselian elements: quantities tabulated for the calculation of accurate predictions of an eclipse or occultation for any point on or above the surface of the Earth. calendar: a system of reckoning time in units of solar days. The days are enumerated according to their position in cyclic patterns usually involving the motions of the Sun and/or the Moon. calendar, Gregorian: The calendar introduced by Pope Gregory XIII in 1582 to replace the Julian calendar. This calendar is now used as the civil calendar in most countries. In the Gregorian calendar, every year that is exactly divisible by four is a leap year, except for centurial years, which must be exactly divisible by 400 to be leap years. Thus 2000 was a leap year, but 1900 and 2100 are not leap years. calendar, Julian: the calendar introduced by Julius Caesar in 46 B.C. to replace the Roman calendar. In the Julian calendar a common year is defined to comprise 365 days, and every fourth year is a leap year comprising 366 days. The Julian calendar was superseded by the Gregorian calendar. calendar, proleptic: the extrapolation of a calendar prior to its date of introduction. catalog equinox: see equinox, catalog. Celestial Ephemeris Origin (CEO): the original name for the Celestial Intermediate Origin (CIO) given in the IAU 2000 resolutions. Obsolete. celestial equator: the plane perpendicular to the Celestial Intermediate Pole (CIP). Colloquially, the projection onto the celestial sphere of the Earth s equator. (See mean equator and equinox; true equator and equinox.) Celestial Intermediate Origin (CIO): the non rotating origin of the Celestial Intermediate Reference System. Formerly referred to as the Celestial Ephemeris Origin (CEO). Celestial Intermediate Origin Locator (CIO Locator): denoted by s, is the difference between the Geocentric Celestial Reference System (GCRS) right ascension and the intermediate right ascension of the intersection of the GCRS and intermediate equators. Celestial Intermediate Pole (CIP): the reference pole of the IAU 2000A precession nutation model. The motions of the CIP are those of the Tisserand mean axis of the Earth with periods greater than two days. (See nutation; precession.) Celestial Intermediate Reference System: a geocentric reference system related to the Geocentric Celestial Reference System (GCRS) by a time dependent rotation taking into account precession nutation. It is defined by the intermediate equator of the Celestial Intermediate Pole (CIP) and the Celestial Intermediate Origin (CIO) on a specific date. celestial pole: see pole, celestial. celestial sphere: an imaginary sphere of arbitrary radius upon which celestial bodies may be considered to be located. As circumstances require, the celestial sphere may be centered at the observer, at the Earth s center, or at any other location. center of figure: that point so situated relative to the apparent figure of a body that any line drawn through it divides the figure into two parts having equal apparent areas. If the body is oddly shaped, the center of figure may lie outside the figure itself. center of light: same as center of figure except referring only to the illuminated portion.
M4 conjunction: the phenomenon in which two bodies have the same apparent ecliptic longitude or right ascension as viewed from a third body. Conjunctions are usually tabulated as geocentric phenomena. For Mercury and Venus, geocentric inferior conjunctions occur when the planet is between the Earth and Sun, and superior conjunctions occur when the Sun is between the planet and Earth. (See longitude, ecliptic.) constellation: 1. A grouping of stars, usually with pictorial or mythical associations, that serves to identify an area of the celestial sphere. 2. One of the precisely defined areas of the celestial sphere, associated with a grouping of stars, that the International Astronomical Union (IAU) has designated as a constellation. Coordinated Universal Time (UTC): the time scale available from broadcast time signals. UTC differs from International Atomic Time (TAI) by an integral number of seconds; it is maintained within ±0 ṣ 9 seconds of UT1 by the introduction of leap seconds. (See International Atomic Time (TAI); leap second; Universal Time (UT).) culmination: the passage of a celestial object across the observer s meridian; also called meridian passage. culmination, lower: (also called culmination below pole for circumpolar stars and the Moon) is the crossing farther from the observer s zenith. culmination, upper: (also called culmination above pole for circumpolar stars and the Moon) or transit is the crossing closer to the observer s zenith. day: an interval of 86 400 SI seconds, unless otherwise indicated. (See second, Système International (SI).) declination: angular distance on the celestial sphere north or south of the celestial equator. It is measured along the hour circle passing through the celestial object. Declination is usually given in combination with right ascension or hour angle. defect of illumination: (sometimes, greatest defect of illumination): the maximum angular width of the unilluminated portion of the apparent disk of a solar system body measured along a radius. deflection of light: the angle by which the direction of a light ray is altered from a straight line by the gravitational field of the Sun or other massive object. As seen from the Earth, objects appear to be deflected radially away from the Sun by up to 1.75 at the Sun s limb. Correction for this effect, which is independent of wavelength, is included in the transformation from mean place to apparent place. deflection of the vertical: the angle between the astronomical vertical and the geodetic vertical. (See astronomical coordinates; geodetic coordinates; zenith.) delta T: see T. delta UT1: see UT1 (or UT). direct motion: for orbital motion in the solar system, motion that is counterclockwise in the orbit as seen from the north pole of the ecliptic; for an object observed on the celestial sphere, motion that is from west to east, resulting from the relative motion of the object and the Earth. diurnal motion: the apparent daily motion, caused by the Earth s rotation, of celestial bodies across the sky from east to west. diurnal parallax: see parallax, geocentric. dynamical equinox: the ascending node of the Earth s mean orbit on the Earth s true equator; i.e., the intersection of the ecliptic with the celestial equator at which the Sun s declination changes from south to north. (See catalog equinox; equinox; true equator and equinox.) dynamical time: the family of time scales introduced in 1984 to replace ephemeris time (ET) as the independent argument of dynamical theories and ephemerides. (See Barycentric Dynamical Time (TDB); Terrestrial Time (TT).) Earth Rotation Angle (ERA): the angle, θ, measured along the equator of the Celestial
M5 Intermediate Pole (CIP) between the direction of he Celestial Intermediate Origin (CIO) and the Terrestrial Intermediate Origin (TIO). It is a linear function of UT1; its time derivative is the Earth s angular velocity. eccentricity: 1. A parameter that specifies the shape of a conic secton. 2. One of the standard elements used to describe an elliptic or hyperbolic orbit. For an elliptical orbit, the quantity e = 1 (b 2 /a 2 ), where a and b are the lengths of the semimajor and semiminor axes, respectively. (See orbital elements.) eclipse: the obscuration of a celestial body caused by its passage through the shadow cast by another body. eclipse, annular: a solar eclipse in which the solar disk is not completely covered but is seen as an annulus or ring at maximum eclipse. An annular eclipse occurs when the apparent disk of the Moon is smaller than that of the Sun. (See eclipse, solar.) eclipse, lunar: an eclipse in which the Moon passes through the shadow cast by the Earth. The eclipse may be total (the Moon passing completely through the Earth s umbra), partial (the Moon passing partially through the Earth s umbra at maximum eclipse), or penumbral (the Moon passing only through the Earth s penumbra). eclipse, solar: actually an occultation of the Sun by the Moon in which the Earth passes through the shadow cast by the Moon. It may be total (observer in the Moon s umbra), partial (observer in the Moon s penumbra), annular, or annular total. (See eclipse, annular.) ecliptic: 1. The mean plane of the orbit of the Earth Moon barycenter around the solar system barycenter. 2. The apparent path of the Sun around the celestial sphere. ecliptic latitude: see latitude, ecliptic. ecliptic longitude: see longitude, ecliptic. elements: a set of parameters used to describe the position and/or motion of an astronomical object. elements, Besselian: see Besselian elements. elements, Keplerian: see Keplerian elements. elements, mean: see mean elements. elements, orbital: see orbital elements. elements, osculating: see osculating elements. elongation: the geocentric angle between two celestial objects. elongation, greatest: the maximum value of a planetary elongation for a solar system body that remains interior to the Earth s orbit, or the maximum value of a satellite elongation. elongation, planetary: the geocentric angle between a planet and the Sun. Planetary elongations are measured from 0 to 180, east or west of the Sun. elongation, satellite: the geocentric angle between a satellite and its primary. Satellite elongations are measured from 0 east or west of the planet. epact: 1. The age of the Moon. 2. The number of days since new moon, diminished by one day, on January 1 in the Gregorian ecclesiastical lunar cycle. (See calendar, Gregorian; lunar phases.) ephemeris: a tabulation of the positions of a celestial object in an orderly sequence for a number of dates. ephemeris hour angle: an hour angle referred to the ephemeris meridian. ephemeris longitude: longitude measured eastward from the ephemeris meridian. (See longitude, terrestrial.) ephemeris meridian: see meridian, ephemeris. ephemeris time (ET): the time scale used prior to 1984 as the independent variable in gravitational theories of the solar system. In 1984, ET was replaced by dynamical time.
M6 ephemeris transit: the passage of a celestial body or point across the ephemeris meridian. epoch: an arbitrary fixed instant of time or date used as a chronological reference datum for calendars, celestial reference systems, star catalogs, or orbital motions. (See calendar; orbit.) equation of the equinoxes: the difference apparent sidereal time minus mean sidereal time, due to the effect of nutation in longitude on the location of the equinox. Equivalently, the difference between the right ascensions of the true and mean equinoxes, expressed in time units. (See sidereal time.) equation of the origins: the arc length, measured positively eastward, from the Celestial Intermediate Origin (CIO) to the equinox along the intermediate equator; alternatively the difference between the Earth Rotation Angle (ERA) and Greenwich Apparent Sidereal Time (ERA GAST). equation of time: the difference apparent solar time minus mean solar time. equator: the great circle on the surface of a body formed by the intersection of the surface with the plane passing through the center of the body perpendicular to the axis of rotation. (See celestial equator.) equinox: 1. Either of the two points on the celestial sphere at which the ecliptic intersects the celestial equator. 2. The time at which the Sun passes through either of these intersection points; i.e., when the apparent ecliptic longitude of the Sun is 0 or 180. 3. The vernal equinox. (See mean equator and equinox; true equator and equinox.) equinox, autumnal: 1. The decending node of the ecliptic on the celestial sphere. 2. The time which the apparent ecliptic longitude of the Sun is 180. equinox, catalog: the intersection of the hour angle of zero right ascension of a star catalog with the celestial equator. Obsolete. equinox, dynamical: the ascending node of the ecliptic on the Earth s true equator. equinox, vernal: 1. The ascending node of the ecliptic on the celestial equator. 2. The time at which the apparent ecliptic longitude of the Sun is 0. era: a system of chronological notation reckoned from a specific event. ERA: see Earth Rotation Angle (ERA). flattening: a parameter that specifies the degree by which a planet s figure differs from that of a sphere; the ratio f = (a b)/a, where a is the equatorial radius and b is the polar radius. frame bias: the orientation of the mean equator and equinox of J2000.0 with respect to the Geocentric Celestial Reference System (GCRS). It is defined by three small and constant angles, two of which describe the offset of the mean pole at J2000.0 and the other is the GCRS right ascension of the mean inertial equinox of J2000.0. frequency: the number of periods of a regular, cyclic phenomenon in a given measure of time, such as a second or a year. (See period; second, Système International (SI); year.) frequency standard: a generator whose output is used as a precise frequency reference; a primary frequency standard is one whose frequency corresponds to the adopted definition of the second, with its specified accuracy achieved without calibration of the device. (See second, Système International (SI).) GAST: see Greenwich Apparent Sidereal Time (GAST). Gaussian gravitational constant: k = 0.017 202 098 95: the constant defining the astronomical system of units of length (astronomical unit (au)), mass (solar mass) and time (day), by means of Kepler s third law. The dimensions of k 2 are those of Newton s constant of gravitation: L 3 M 1 T 2. geocentric: with reference to, or pertaining to, the center of the Earth. Geocentric Celestial Reference System (GCRS): a system of geocentric space time coordinates within the framework of General Relativity. The metric tensor used in the system is specified by the IAU 2000 resolutions. The GCRS is defined such that its spatial coordinates
M7 are kinematically non rotating with respect to those of the Barycentric Celestial Reference System (BCRS). (See Geocentric Coordinate Time (TCG).) Geocentric Coordinate Time (TCG): the coordinate time of the Geocentric Celestial Reference System (GCRS), which advances by SI seconds within that system. TCG is related to Barycentric Coordinate Time (TCB) and Terrestrial Time (TT), by relativistic transformations that include a secular term. (See second, Système International (SI).) geocentric coordinates: 1. The latitude and longitude of a point on the Earth s surface relative to the center of the Earth. 2. Celestial coordinates given with respect to the center of the Earth. (See latitude, terrestrial; longitude, terrestrial; zenith.) geocentric zenith: see zenith, geocentric. geodetic coordinates: the latitude and longitude of a point on the Earth s surface determined from the geodetic vertical (normal to the reference ellipsoid). (See latitude, terrestrial; longitude, terrestrial; zenith.) geodetic zenith: see zenith, geodetic. geoid: an equipotential surface that coincides with mean sea level in the open ocean. On land it is the level surface that would be assumed by water in an imaginary network of frictionless channels connected to the ocean. geometric position: the position of an object defined by a straight line (vector) between the center of the Earth (or the observer) and the object at a given time, without any corrections for light time, aberration, etc. GHA: see Greenwich Hour Angle (GHA). GMST: see Greenwich Mean Sidereal Time (GMST). greatest defect of illumination: see defect of illumination. Greenwich Apparent Sidereal Time (GAST): the Greenwich hour angle of the true equinox of date. Greenwich Hour Angle (GHA): angular distance on the celestial sphere measured westward along the celestial equator from the Greenwich meridian to the hour circle that passes through a celestial object or point. Greenwich Mean Sidereal Time (GMST): the Greenwich hour angle of the mean equinox of date. Greenwich meridian: see meridian, Greenwich. Greenwich sidereal date (GSD): the number of sidereal days elapsed at Greenwich since the beginning of the Greenwich sidereal day that was in progress at the Julian date (JD) 0.0. Greenwich sidereal day number: the integral part of the Greenwich sidereal date (GSD). Gregorian calendar: see calendar, Gregorian. height: the distance above or below a reference surface such as mean sea level on the Earth or a planetographic reference surface on another solar system planet. heliocentric: with reference to, or pertaining to, the center of the Sun. heliocentric parallax: see parallax, heliocentric. horizon: 1. A plane perpendicular to the line from an observer through the zenith. 2. The observed border between Earth and the sky. horizon, astronomical: the plane perpendicular to the line from an observer to the astronomical zenith that passes through the point of observation. horizon, geocentric: the plane perpendicular to the line from an observer to the geocentric zenith that passes through the center of the Earth. horizon, natural: the border between the sky and the Earth as seen from an observation point. horizontal parallax: see parallax, horizontal. horizontal refraction: see refraction, horizontal.
M8 hour angle: angular distance on the celestial sphere measured westward along the celestial equator from the meridian to the hour circle that passes through a celestial object. hour circle: a great circle on the celestial sphere that passes through the celestial poles and is therefore perpendicular to the celestial equator. IAU: see International Astronomical Union (IAU). illuminated extent: the illuminated area of an apparent planetary disk, expressed as a solid angle. inclination: 1. The angle between two planes or their poles. 2. Usually, the angle between an orbital plane and a reference plane. 3. One of the standard orbital elements that specifies the orientation of the orbit. (See orbital elements.) instantaneous orbit: see orbit, instantaneous. intercalate: to insert an interval of time (e.g., a day or a month) within a calendar, usually so that it is synchronized with some natural phenomenon such as the seasons or lunar phases. intermediate place (or position): the proper place of an object expressed with respect to the true (intermediate) equator and CIO of date. International Astronomical Union (IAU): an international non governmental organization that promotes the science of astronomy. The IAU is composed of both national and individual members. In the field of positional astronomy, the IAU, among other activities, recommends standards for data analysis and modeling, usually in the form of resolutions passed at General Assemblies held every three years. International Atomic Time (TAI): the continuous time scale resulting from analysis by the Bureau International des Poids et Mesures of atomic time standards in many countries. The fundamental unit of TAI is the SI second on the geoid, and the epoch is 1958 January 1. (See second, Système International (SI).) International Celestial Reference Frame (ICRF): 1. A set of extragalactic objects whose adopted positions and uncertainties realize the International Celestial Reference System (ICRS) axes and give the uncertainties of those axes. 2. The name of the radio catalog whose 212 defining sources serve as fiducial points to fix the axes of the ICRS, recommended by the International Astronomical Union (IAU) in 1997. International Celestial Reference System (ICRS): a time independent, kinematically nonrotating barycentric reference system recommended by the International Astronomical Union (IAU) in 1997. Its axes are those of the International Celestial Reference Frame (ICRF). international meridian: see meridian, Greenwich. International Terrestrial Reference Frame (ITRF): a set of reference points on the surface of the Earth whose adopted positions and velocities fix the rotating axes of the International Terrestrial Reference System (ITRS). International Terrestrial Reference System (ITRS): a time dependent, non inertial reference system co moving with the geocenter and rotating with the Earth. The ITRS is the recommended system in which to express positions on the Earth. invariable plane: the plane through the center of mass of the solar system perpendicular to the angular momentum vector of the solar system. irradiation: an optical effect of contrast that makes bright objects viewed against a dark background appear to be larger than they really are. Julian calendar: see calendar, Julian. Julian date (JD): the interval of time in days and fractions of a day, since 4713 B.C. January 1, Greenwich noon, Julian proleptic calendar. In precise work, the timescale, e.g., Terrestrial Time (TT) or Universal Time (UT), should be specified. Julian date, modified (MJD): the Julian date (JD) minus 2400000.5. Julian day number: the integral part of the Julian date (JD).
M9 Julian year: see year, Julian. Keplerian elements: a certain set of six orbital elements, sometimes referred to as the Keplerian set. Historically, this set included the mean anomaly at the epoch, the semimajor axis, the eccentricity and three Euler angles: the longitude of the ascending node, the inclination, and the argument of pericenter. The time of pericenter passage is often used as part of the Keplerian set instead of the mean anomaly at the epoch. Sometimes the longitude of pericenter (which is the sum of the longitude of the ascending node and the argument of pericenter) is used instead of either the longitude of the ascending node or the argument of pericenter. Laplacian plane: 1. For planets see invariable plane. 2. For a system of satellites, the fixed plane relative to which the vector sum of the disturbing forces has no orthogonal component. latitude, celestial: see latitude, ecliptic. latitude, ecliptic: angular distance on the celestial sphere measured north or south of the ecliptic along the great circle passing through the poles of the ecliptic and the celestial object. Also referred to as celestial latitude. latitude, terrestrial: angular distance on the Earth measured north or south of the equator along the meridian of a geographic location. leap second: a second inserted as the 61 st second of a minute at announced times to keep UTC within 0 ṣ 9 of UT1. Generally, leap seconds are added at the end of June or December as necessary, but may be inserted at the end of any month. Although it has never been utilized, it is possible to have a negative leap second in which case the 60 th second of a minute would be removed. (See Coordinated Universal Time (UTC); second, Système International (SI); Universal Time (UT).) librations: the real or apparent oscillations of a body around a reference point. When referring to the Moon, librations are variations in the orientation of the Moon s surface with respect to an observer on the Earth. Physical librations are due to variations in the orientation of the Moon s rotational axis in inertial space. The much larger optical librations are due to variations in the rate of the Moon s orbital motion, the obliquity of the Moon s equator to its orbital plane, and the diurnal changes of geometric perspective of an observer on the Earth s surface. light time: the interval of time required for light to travel from a celestial body to the Earth. light time displacement: the difference between the geometric and astrometric place of a solar system body. It is caused by the motion of the body during the interval it takes light to travel from the body to Earth. light year: the distance that light traverses in a vacuum during one year. Since there are various ways to define a year, there is an ambiguity in the exact distance; the IAU recommends using the Julian year as the time basis. A light year is approximately 9.46 10 12 km, 5.88 10 12 statute miles, 6.32 10 4 au, and 3.07 10 1 parsecs. Often distances beyond the solar system are given in parsecs. (See parsec.) light, deflection of: see deflection of light. limb: the apparent edge of the Sun, Moon, or a planet or any other celestial body with a detectable disk. limb correction: generally, a small angle (positive or negative) that is added to the tabulated apparent semidiameter of a body to compensate for local topography at a specific point along the limb. Specifically for the Moon, the angle taken from the Watts lunar limb data (Watts, C. B., APAE XVII, 1963) that is used to correct the semidiameter of the Watts mean limb. The correction is a function of position along the limb and the apparent librations. The Watts mean limb is a circle whose center is offset by about 0.6 from the direction of the Moon s center of mass and whose radius is about 0.4 greater than the semidiameter of the Moon that is computed based on its IAU adopted radius in kilometers. local sidereal time: the hour angle of the vernal equinox with respect to the local meridian.
M10 longitude of the ascending node: given an orbit and a reference plane through the primary body (or center of mass): the angle, Ω, at the primary, between a fiducial direction in the reference plane and the point at which the orbit crosses the reference plane from south to north. Equivalently, Ω is one of the angles in the reference plane between the fiducial direction and the line of nodes. It is one of the six Keplerian elements that specify an orbit. For planetary orbits, the primary is the Sun, the reference plane is usually the ecliptic, and the fiducial direction is usually toward the equinox. (See node; orbital elements.) longitude, celestial: see longitude, ecliptic. longitude, ecliptic: angular distance on the celestial sphere measured eastward along the ecliptic from the dynamical equinox to the great circle passing through the poles of the ecliptic and the celestial object. Also referred to as celestial longitude. longitude, terrestrial: angular distance measured along the Earth s equator from the Greenwich meridian to the meridian of a geographic location. luminosity class: distinctions in intrinsic brightness among stars of the same spectral type, typically given as a Roman numeral. It denotes if a star is a supergiant (Ia or Ib), giant (II or III), subgiant (IV), or main sequence also called dwarf (V). Sometimes subdwarfs (VI) and white dwarfs (VII) are regarded as luminosity classes. (See spectral types or classes.) lunar phases: cyclically recurring apparent forms of the Moon. New moon, first quarter, full moon and last quarter are defined as the times at which the excess of the apparent ecliptic longitude of the Moon over that of the Sun is 0, 90, 180 and 270, respectively. (See longitude, ecliptic.) lunation: the period of time between two consecutive new moons. magnitude of a lunar eclipse: the fraction of the lunar diameter obscured by the shadow of the Earth at the greatest phase of a lunar eclipse, measured along the common diameter. (See eclipse, lunar.) magnitude of a solar eclipse: the fraction of the solar diameter obscured by the Moon at the greatest phase of a solar eclipse, measured along the common diameter. (See eclipse, solar.) magnitude, stellar: a measure on a logarithmic scale of the brightness of a celestial object. Since brightness varies with wavelength, often a wavelength band is specified. A factor of 100 in brightness is equivalent to a change of 5 in stellar magnitude, and brighter sources have lower magnitudes. For example, the bright star Sirius has a visual band magnitude of 1.46 whereas the faintest stars detectable with an unaided eye under ideal conditions have visual band magnitudes of about 6.0. mean distance: an average distance between the primary and the secondary gravitating body. The meaning of the mean distance depends upon the chosen method of averaging (i.e., averaging over the time, or over the true anomaly, or the mean anomaly. It is also important what power of the distance is subject to averaging.) In this volume the mean distance is defined as the inverse of the time averaged reciprocal distance: ( r 1 dt) 1. In the two body setting, when the disturbances are neglected and the orbit is elliptic, this formula yields the semimajor axis, a, which plays the role of mean distance. mean elements: average values of the orbital elements over some section of the orbit or over some interval of time. They are interpreted as the elements of some reference (mean) orbit that approximates the actual one and, thus, may serve as the basis for calculating orbit perturbations. The values of mean elements depend upon the chosen method of averaging and upon the length of time over which the averaging is made. mean equator and equinox: the celestial coordinate system defined by the orientation of the Earth s equatorial plane on some specified date together with the direction of the dynamical equinox on that date, neglecting nutation. Thus, the mean equator and equinox moves in response only to precession. Positions in a star catalog have traditionally been referred to a
M11 catalog equator and equinox that approximate the mean equator and equinox of a standard epoch. (See catalog equinox; true equator and equinox.) mean motion: in undisturbed elliptic motion, the constant angular speed required for a body to complete one revolution in an orbit of a specified semimajor axis. mean place: coordinates of a star or other celestial object (outside the solar system) at a specific date, in the Barycentric Celestial Reference System (BCRS). Conceptually, the coordinates represent the direction of the object as it would hypothetically be observed from the solar system barycenter at the specified date, with respect to a fixed coordinate system (e.g., the axes of the International Celestial Reference Frame (ICRF)), if the masses of the Sun and other solar system bodies were negligible. mean solar time: see solar time, mean. meridian: a great circle passing through the celestial poles and through the zenith of any location on Earth. For planetary observations a meridian is half the great circle passing through the planet s poles and through any location on the planet. meridian, ephemeris: a fictitious meridian that rotates independently of the Earth at the uniform rate implicitly defined by Terrestrial Time (TT). The ephemeris meridian is 1.002 738 T east of the Greenwich meridian, where T = TT UT1. meridian, Greenwich: (also called international or prime meridian) is a generic reference to one of several origins of the Earth s longitude coordinate (zero longitude). In The Astronomical Almanac, it is the plane defining the astronomical zero meridian; it contains the geocenter, the Celestial Intermediate Pole and the Terrestrial Intermediate Origin. Other definitions are: the x z plane of the International Terrestrial Reference System (ITRS); the zero longitude meridian of the World Geodetic System 1984 (WGS 84); and the meridian that passes through the transit circle at the Royal Observatory, Greenwich. Note that the latter meridian is about 100 m west of the others. meridian, international: see meridian, Greenwich. meridian, prime: on Earth, same as Greenwich meridian. On other solar system objects, the zero longitude meridian, typically defined via international convention by an observable surface feature or rotational elements. month: a calendrical unit that approximates the period of revolution of the Moon. Also, the period of time between the same dates in successive calendar months. month, sidereal: the period of revolution of the Moon about the Earth (or Earth Moon barycenter) in a fixed reference frame. It is the mean period of revolution with respect to the background stars. The mean length of the sidereal month is approximately 27.322 days. month, synodic: the period between successive new Moons (as seen from the geocenter). The mean length of the synodic month is approximately 29.531 days. moonrise, moonset: the times at which the apparent upper limb of the Moon is on the astronomical horizon. In The Astronomical Almanac, they are computed as the times when the true zenith distance, referred to the center of the Earth, of the central point of the Moon s disk is 90 34 + s π, where s is the Moon s semidiameter, π is the horizontal parallax, and 34 is the adopted value of horizontal refraction. nadir: the point on the celestial sphere diametrically opposite to the zenith. node: either of the points on the celestial sphere at which the plane of an orbit intersects a reference plane. The position of one of the nodes (the longitude of the ascending node) is traditionally used as one of the standard orbital elements. nutation: oscillations in the motion of the rotation pole of a freely rotating body that is undergoing torque from external gravitational forces. Nutation of the Earth s pole is specified in terms of components in obliquity and longitude.
M12 obliquity: in general, the angle between the equatorial and orbital planes of a body or, equivalently, between the rotational and orbital poles. For the Earth the obliquity of the ecliptic is the angle between the planes of the equator and the ecliptic; its value is approximately 23.44. occultation: the obscuration of one celestial body by another of greater apparent diameter; especially the passage of the Moon in front of a star or planet, or the disappearance of a satellite behind the disk of its primary. If the primary source of illumination of a reflecting body is cut off by the occultation, the phenomenon is also called an eclipse. The occultation of the Sun by the Moon is a solar eclipse. (See eclipse, solar.) opposition: the phenomenon whereby two bodies have apparent ecliptic longitudes or right ascensions that differ by 180 as viewed by a third body. Oppositions are usually tabulated as geocentric phenomena. orbit: the path in space followed by a celestial body as a function of time. (See orbital elements.) orbit, elliptical: a closed orbit with an eccentricity less than 1. orbit, hyperbolic: an open orbit with an eccentricity greater than 1. orbit, instantaneous: the unperturbed two body orbit that a body would follow if perturbations were to cease instantaneously. Each orbit in the solar system (and, more generally, in any perturbed two body setting) can be represented as a sequence of instantaneous ellipses or hyperbolae whose parameters are called orbital elements. If these elements are chosen to be osculating, each instantaneous orbit is tangential to the physical orbit. (See orbital elements; osculating elements.) orbit, parabolic: an open orbit with an eccentricity of 1. orbital elements: a set of six independent parameters that specifies an instantaneous orbit. Every real orbit can be represented as a sequence of instantaneous ellipses or hyperbolae sharing one of their foci. At each instant of time, the position and velocity of the body is characterised by its place on one such instantaneous curve. The evolution of this representation is mathematically described by evolution of the values of orbital elements. Different sets of geometric parameters may be chosen to play the role of orbital elements. The set of Keplerian elements is one of many such sets. When the Lagrange constraint (the requirement that the instantaneous orbit is tangential to the actual orbit) is imposed upon the orbital elements, they are called osculating elements. osculating elements: a set of parameters that specifies the instantaneous position and velocity of a celestial body in its perturbed orbit. Osculating elements describe the unperturbed (twobody) orbit that the body would follow if perturbations were to cease instantaneously. (See orbit, instantaneous; orbital elements.) parallax: the difference in apparent direction of an object as seen from two different locations; conversely, the angle at the object that is subtended by the line joining two designated points. parallax, annual: see parallax, heliocentric. parallax, diurnal: see parallax, geocentric. parallax, geocentric: the angular difference between the topocentric and geocentric directions toward an object. Also called diurnal parallax. parallax, heliocentric: the angular difference between the geocentric and heliocentric directions toward an object; it is the angle subtended at the observed object. Also called annual parallax. parallax, horizontal: the angular difference between the topocentric and a geocentric direction toward an object when the object is on the astronomical horizon. parallax, solar: the angular width subtended by the Earth s equatorial radius when the Earth is at a distance of 1 astronomical unit (au). The value for the solar parallax is 8.794143 arcseconds.
M13 parallax in altitude: the angular difference between the topocentric and geocentric direction toward an object when the object is at a given altitude. parsec: the distance at which one astronomical unit (au) subtends an angle of one arcsecond; equivalently the distance to an object having an annual parallax of one arcsecond. One parsec is 1/sin (1 ) = 206264.806 au, or about 3.26 light years. penumbra: 1. The portion of a shadow in which light from an extended source is partially but not completely cut off by an intervening body. 2. The area of partial shadow surrounding the umbra. pericenter: the point in an orbit that is nearest to the origin of the reference system. (See perigee; perihelion.) pericenter, argument of: one of the Keplerian elements. It is the angle measured in the orbit plane from the ascending node of a reference plane (usually the ecliptic) to the pericenter. perigee: the point in an orbit that is nearest to the Earth. Perigee is sometimes used with reference to the apparent orbit of the Sun around the Earth. perihelion: the point in an orbit that is nearest to the Sun. period: the interval of time required to complete one revolution in an orbit or one cycle of a periodic phenomenon, such as a cycle of phases. (See phase.) perturbations: 1. Deviations between the actual orbit of a celestial body and an assumed reference orbit. 2. The forces that cause deviations between the actual and reference orbits. Perturbations, according to the first meaning, are usually calculated as quantities to be added to the coordinates of the reference orbit to obtain the precise coordinates. phase: 1. The name applied to the apparent degree of illumination of the disk of the Moon or a planet as seen from Earth (cresent, gibbous, full, etc.). 2. The ratio of the illuminated area of the apparent disk of a celestial body to the entire area of the apparent disk; i.e., the fraction illuminated. 3. Used loosely to refer to one aspect of an eclipse (partial phase, annular phase, etc.). (See lunar phases.) phase angle: the angle measured at the center of an illuminated body between the light source and the observer. photometry: a measurement of the intensity of light, usually specified for a specific wavelength range. planetocentric coordinates: coordinates for general use, where the z axis is the mean axis of rotation, the x axis is the intersection of the planetary equator (normal to the z axis through the center of mass) and an arbitrary prime meridian, and the y axis completes a right hand coordinate system. Longitude of a point is measured positive to the prime meridian as defined by rotational elements. Latitude of a point is the angle between the planetary equator and a line to the center of mass. The radius is measured from the center of mass to the surface point. planetographic coordinates: coordinates for cartographic purposes dependent on an equipotential surface as a reference surface. Longitude of a point is measured in the direction opposite to the rotation (positive to the west for direct rotation) from the cartographic position of the prime meridian defined by a clearly observable surface feature. Latitude of a point is the angle between the planetary equator (normal to the z axis and through the center of mass) and normal to the reference surface at the point. The height of a point is specified as the distance above a point with the same longitude and latitude on the reference surface. polar motion: the quasi periodic motion of the Earth s pole of rotation with respect to the Earth s solid body. More precisely, the angular excursion of the CIP from the ITRS z axis. (See Celestial Intermediate Pole (CIP); International Terrestrial Reference System (ITRS).) polar wobble: see wobble, polar. pole, celestial: either of the two points projected onto the celestial sphere by the Earth s axis. Usually, this is the axis of the Celestial Intermediate Pole (CIP), but it may also refer to the
M14 instantaneous axis of rotation, or the angular momentum vector. All of these axes are within 0.1 of each other. If greater accuracy is desired, the specific axis should be designated. pole, Tisserand mean: the angular momentum pole for the Earth about which the total internal angular momentum of the Earth is zero. The motions of the Celestial Intermediate Pole (CIP) (described by the conventional theories of precession and nutation) are those of the Tisserand mean pole with periods greater than two days in a celestial reference system (specifically, the Geocentric Celestial Reference System (GCRS)). precession: the smoothly changing orientation (secular motion) of an orbital plane or the equator of a rotating body. Applied to rotational dynamics, precession may be excited by a singular event, such as a collision, a progenitor s disruption, or a tidal interaction at a close approach (free precession); or caused by continuous torques from other solar system bodies, or jetting, in the case of comets (forced precession). For the Earth s rotation, the main sources of forced precession are the torques caused by the attraction of the Sun and Moon on the Earth s equatorial bulge, called precession of the equator (formerly known as lunisolar precession). The slow change in the orientation of the Earth s orbital plane is called precession of the ecliptic (formerly known as planetary precession). The combination of both motions that is, the motion of the equator with respect to the ecliptic is called general precession. prime meridian: see meridian, prime. proleptic calendar: see calendar, proleptic. proper motion: the projection onto the celestial sphere of the space motion of a star relative to the solar system; thus the transverse component of the space motion of a star with respect to the solar system. Proper motion is usually tabulated in star catalogs as changes in right ascension and declination per year or century. proper place: direction of an object in the GCRS that takes into account orbital or space motion and light time (as applicable), light deflection, and annual aberration. Thus, the position (geocentric right ascension and declination) at which the object would actually be seen from the center of the Earth if the Earth were transparent, non refracting, and massless. Unless otherwise stated, the coordinates are expressed with respect to the GCRS axes, which are derived from those of the ICRS. quadrature: a configuration in which two celestial bodies have apparent longitudes that differ by 90 as viewed from a third body. Quadratures are usually tabulated with respect to the Sun as viewed from the center of the Earth. (See longitude, ecliptic.) radial velocity: the rate of change of the distance to an object, usually corrected for the Earth s motion with respect to the solar system barycenter. radius vector: an imaginary line from the center of one body to another, often from the heliocenter. Sometimes only the length of the vector is given. refraction: the change in direction of travel (bending) of a light ray as it passes obliquely from a medium of lesser/greater density to a medium of greater/lesser density. refraction, astronomical: the change in direction of travel (bending) of a light ray as it passes obliquely through the atmosphere. As a result of refraction the observed altitude of a celestial object is greater than its geometric altitude. The amount of refraction depends on the altitude of the object and on atmospheric conditions. refraction, horizontal: the astronomical refraction at the astronomical horizon; often, an adopted value of 34 is used in computations for sea level observations. retrograde motion: for orbital motion in the solar system, motion that is clockwise in the orbit as seen from the north pole of the ecliptic; for an object observed on the celestial sphere, motion that is from east to west, resulting from the relative motion of the object and the Earth. (See direct motion.) right ascension: angular distance on the celestial sphere measured eastward along the celestial